Spacetimes with longitudinal and angular magnetic fields in third order Lovelock gravity

Abstract

We obtain two new classes of magnetic brane solutions in third order Lovelock gravity. The first class of solutions yields an (n + 1)-dimensional spacetime with a longitudinal magnetic field generated by a static source. We generalize this class of solutions to the case of spinning magnetic branes with one or more rotation parameters. These solutions have no curvature singularity and no horizons, but have a conic geometry. For the spinning brane, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters, while the static brane has no net electric charge. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Although the second class of solutions may be made electrically charged by a boost transformation, the transformed solutions do not present new spacetimes. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes. * email address: mhd@shirazu.ac.ir

Magnetic branes supported by a nonlinear electromagnetic field

“…Solutions with longitudinal and angular magnetic field were considered in Refs. [9][10][11][12]. Similar static solutions in the context of cosmic string theory were found in Ref.…”

Accelerating Cosmologies in Lovelock Gravity with Dilaton~!2009-08-20~!2009-09-23~!2010-06-03~!

“…Solutions for more complicated variants of the theory are not large in number. Investigations of third order Lovelock gravity (without dilaton) can be found in [10,11,12], studies of the second order with dilaton can be found in [13,14]. Moreover, C. C. Briggs obtains explicit formulae for the 4-th and 5-th Lovelock tensors.…”

Diagrammatic derivation of Lovelock densities

“…As a result, up to now only the lowest order Lovelock correction, i.e. the Gauss-Bonnet term, has been extensively studied [16,17], with recent attempts to also include a third and fourth order density [18,19,20,21].In this letter we discuss an alternative method of calculating the first Lovelock densities, based on the use of permutation diagrams, instead of the more conventional way of using the Kronecker permutation tensor. We demonstrate that this method can lead to dramatic simplification of certain calculations, rendering the derivation of the first few scalar densities almost trivial.…”

“…As a result, up to now only the lowest order Lovelock correction, i.e. the Gauss-Bonnet term, has been extensively studied [16,17], with recent attempts to also include a third and fourth order density [18,19,20,21].…”